On certain properties of some subclasses of univalent functions

Milutin Obradovic, Nikola Tuneski

Abstract


In this paper we determine the disks \(|z|<r\le1\) where for different classes of univalent functions, we have the property
\[{\rm Re}\left\{2\frac{zf'(z)}{f(z)}-\frac{z f''(z)}{f'(z)}\right\}>0\qquad (|z|<r).\]


Keywords


univalent, inverse functions, coefficients, sharp bound

Full Text:

PDF

References


P.L. Duren, Univalent function, Springer-Verlag, New York, 1983.

I. Jovanovic and M. Obradovic, A note on certain classes of univalent functions, Filomat 9 (1995), no. 1, 69-72.

S. Miller, P. Mocanu and M.O. Reade, All alpha-convex functions are univalent and starlike, Proc. Amer. Math. Soc. 37 (1973), 553-554.

M. Obradovic and S. Ponnusamy, New criteria and distortion theorems for univalent functions, Complex Variables Theory Appl. 44 (2001), 173-191.

M. Obradovic and S. Ponnusamy, On the class U, Proc. 21st Annual Conference of the Jammu Math. Soc. and a National Seminar on Analysis and its Application, 11-26, 2011.

M. Obradovic and S. Ponnusamy, Radius properties for subclasses of univalent functions, Analysis 25 (2005), 183-188.

M. Obradovic, S. Ponnusamy and K.J. Wirths, Coefficients characterisations and se3ctions for some univalent functions, Siberian Math. J. 54 (2013), no.4, 679-696.

M. Obradovic and N. Tuneski, Some properties of the class U, Ann. Univ. MariaeCurie-Sk lodowska 73, sectio A, (2019), no.1, 49-56.

D.K. Thomas, N. Tuneski, A. Vasudevarao, Univalent Functions: A Primer, De Gruyter Studies in Mathematics, 69, De Gruyter, Berlin, Boston, 2018.




DOI: http://dx.doi.org/10.24193/subbmath.2023.4.06

Refbacks

  • There are currently no refbacks.